The apparent lack of massive O-type stars near the zero-age main sequence (at ages < 2 Myr) is a topic widely discussed. Different explanations for this elusive detection have been proposed, but no firm conclusions have been reached yet. We reassess this empirical result benefiting from the high-quality spectroscopic observations of >400 Galactic O-type stars gathered by the IACOB and OWN surveys. We used temperatures and gravities from a iacob-gbat/fastwind spectroscopic analysis to locate our sample in the Kiel and spectroscopic HR diagrams. We evaluated the completeness of our sample of stars, observational biases using information from the Galactic O star catalog (GOSC), systematics of our methodology, and compare with other recent studies using smaller samples of Galactic O-type stars. We base our discussion on the spectroscopic HR diagram to avoid the use of uncertain distances. We performed a detailed study of the young cluster Trumpler-14 as an example of how Gaia cluster distances can help to construct the associated classical HR diagram. The apparent lack of massive O-type stars near the ZAMS with masses between 30 and 70 Msol persist even when spectroscopic results from a large, non-biased sample of stars are used. We do not find correlation between the dearth of stars and observational biases, limitations of our methodology, or the use of spectroscopic HR diagram instead of the classical one. Investigating the efficiency of mass accretion during the formation process we conclude that an adjustment of the accretion rate towards lower values could reconcile the hotter boundary of detected O-type stars and the theoretical birthline. Last, we discuss that the presence of a small sample of O2-O3.5 stars found closer to the ZAMS might be explained taking into account non-standard star evolution (e.g. binary interaction, mergers, or homogeneous evolution).